Area 1:2:3
Construct a point M inside △ABC such that the areas of △ABM, △BCM, and △CAM are in ratio 1:2:3.
Hint:
Use that altitudes from M in △ABM, △BCM, and △CAM are 1/6, 1/3, and 1/2 of the corresponding altitude of △ABC.
Alternatively, use the the first part of Exercise 20.24.